It won’t be easy, you’ll think it strange/ When I try to explain how I feel.

The opening lines of “Don’t Cry for Me Argentina” seem like the right musical accompaniment for investors as they shed money, and maybe a few tears, over emerging markets.

Explaining the turmoil that has gripped Argentina, Turkey, Thailand and other developing economies won’t be easy, but you’ll think it strange that many smart fund managers aren’t recommending a complete retreat from emerging markets.

The facts are pretty stark. Emerging-market stocks lost nearly 7% in January alone, many currencies got hammered and central banks had to resort to emergency measures to stanch the bleeding. Unsurprisingly, investors bailed. Exchange-traded funds that focus on emerging-market stocks saw their second-biggest withdrawal on record in the week ended Jan. 29, according to Lipper.

The withdrawal of U.S. monetary stimulus and the sputtering noises made by China, which accounts for more than 10% of global gross domestic product (and around a third of emerging markets’ GDP), focused investors’ minds. Economies with bad fundamentals-large current-account deficits, weak growth, political instability-became pariahs.

Some investors are already at their wits’ end. One money manager late on Friday confessed to wanting to “just lie down on the floor” to recover from a brutal week. For those still standing, the next move will depend on choice of assets and stomach for a roller-coaster ride. Assuming the Fed stays the course and China’s economy holds up, here is a possible roadmap through the emerging-markets maze.

“I am very busy and very bullish on emerging markets.” The prize for the most surprising quote of last week has to go to Adrian Mowat, chief emerging-market and Asian equity strategist at J.P. Morgan Chase & Co.

In his view, tighter U.S. monetary policy could actually be good for emerging markets if it coincides with stronger economic growth. He also believes that the world economy’s reliance on China is overstated.

In addition, the recent fall in emerging-market stocks has made some companies cheap. Mr. Mowat estimates that stocks in emerging economies are trading at a discount of 36% to their U.S. counterparts, compared with a historic average of 20%. His year-end forecast for the benchmark MSCI Emerging Markets Index is some 28% above the current levels. Among J.P. Morgan’s top picks are Russian energy company OAO Gazprom, large Russian lender OAO Sberbank, and Hyundai Motor Co. of South Korea.

It is fair to say that Mr. Mowat is a lone voice in a chorus of bearishness.

Some experts, like Jay Pelosky, are downright apocalyptic. Mr. Pelosky, whose firm J2Z Advisory LLC advises funds with around $3 billion under management, last week held a call with clients titled: “Global Economy Snatches Defeat from the Jaws of Victory.”

“The chances of a synchronized global recovery have been killed by what is going on in emerging markets,” Mr. Pelosky told me. “The growth models are all broken, whether they are in Europe, the U.S. or emerging markets.” His recipe to survive these gloomy times: short oil to profit from an expected slowdown in global growth while buying gold-mining companies and long-dated U.S. municipal bonds and Treasurys.

Others aren’t ready to adopt a completely defensive posture just yet. In recent weeks, Sara Zervos, the head of the global debt team at OppenheimerFunds, asked herself a simple question: “Who’s left with no clothes on in the swimming pool?” As the turmoil deepened, more and more countries were left exposed and Ms. Zervos, whose team manages more than $18 billion, shifted her gaze from government bonds to corporate paper. She believes that savvy investors can find good value among highly rated emerging-market companies.

A common thread among these disparate views is to keep an eye on the long term. As policies and risk appetites change, we are witnessing a major shift in capital flows that will shape the investment landscape for a world without substantial central-bank stimulus.

Marc Chandler, global head currency strategist at Brown Brothers Harriman, a custodian for over $3 trillion in assets, believes that this shake-out will prompt “tourist investors” to leave, but that less flighty dollars will stay.

“This is a long-term unwinding of capital flows which will take two or three years to complete,” he says. Or as Evita would put it: “I had to let it happen, I had to change.”